In dioecious populations, males and females may evolve different trait values to increase fitness through their respective sexual functions. Because hermaphrodites express both sexual functions, resolving sexual conflict is potentially more difficult for them. Here, we show that hermaphrodite plants can partially resolve sexual conflict by expressing different trait values in different male and female modules (e.g., different flowers, inflorescences, branches, etc). We analyzed the flowering phenology, sex allocation, and selection gradients on floral traits of flowers of the andromonoecious plant Pulsatilla alpina, which produces both bisexual and male flowers. Our results indicate that strong protogyny prevents early bisexual flowers from profiting from high siring opportunities early in the reproductive season at a time when male flowers could achieve high siring success. The production of unisexual male flowers thus resolves this sexual conflict because it allows the flowers to express their male function without waiting until after the female function has been performed. Our study illustrates the resolution of sexual conflict arising from phenological constraints via modular divergence in sex allocation. We discuss the extent to which modular variation in sex allocation in the context of other sexual systems may be similarly explained.